Cambridge International Mathematics

Assumed Knowledge (Geometry and graphs) 5

SPECIAL QUADRILATERALS

There are six special quadrilaterals:

The following properties of quadrilaterals are useful:

PARALLELOGRAM

In any parallelogram: ² opposite sides are equal in length

² opposite angles are equal in size

² diagonals bisect each other.

RHOMBUS

In any rhombus: ² opposite sides are parallel

² opposite angles are equal in size

² diagonals bisect each other at right angles

² diagonals bisect the angles at each vertex.

RECTANGLE

In any rectangle: ² opposite sides are equal in length

² diagonals are equal in length

² diagonals bisect each other.

KITE

In any kite: ² two pairs of adjacent sides are equal

² the diagonals are perpendicular

² one diagonal splits the kite into two

isosceles triangles.

SQUARE

In any square: ² opposite sides are parallel

² all sides are equal in length

² all angles are right angles

² diagonals bisect each other at right angles

² diagonals bisect the angles at each vertex.

parallelogram rectangle rhombus square trapezium kite

² Aparallelogramis a quadrilateral which has opposite sides parallel.

² Arectangleis a parallelogram with four equal angles of 90 o.

² Arhombusis a quadrilateral in which all sides are equal.

² Asquareis a rhombus with four equal angles of 90 o.

² Atrapeziumis a quadrilateral which has exactly one pair of parallel sides.

² Akiteis a quadrilateral which has two pairs of equal adjacent sides.

IGCSE01

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